I don't have Cats on my 350TBI either, had to drop the stock exhaust due to significant damage on the last offroad trip I went on. running headers and dual pipes with mufflers only. Drives fine, no computer issues related to lack of Cats.
The only real engines that need the Cats or reprogramming without them are the ones running after Cat 02 sensors, and all those are for are to make sure the Cat is working properly. I just went through that crap with my dads car, the factory Cat had burnt out and was throwing the SES light. that after cat sensor is set for a specific temp setting after the gasses are worked over in the Cat. Replaced the burnt out (hollowed out) Cat with a new "used" one and everything worked fine and passed the plug & play emissions testing here in Phoenix..
Right now the truck is in Inidiana, where they don't do any sort of emissions testing or any type of vehicle inspections, so in reality, no one would really know about it's lack of converters.